“…Simple modifications to a conventional IRT model are not likely to account for the potential subpopulations and individual differences that manifest in Figure 1. This research attempts to address the challenges of modeling multivariate count data with inflation and heaping by combining methodological approaches from three distinct but related literatures: IRT models for multivariate count data (L. Wang, 2010), latent variable models for heaping (H. Wang & Heitjan, 2008) and extreme responding (Böckenholt, 2012;Bolt & Johnson, 2009;De Boeck & Partchev, 2012;Thissen-Roe & Thissen, 2013), and mixture IRT models (Finch & Pierson, 2011;Finkelman, Green, Gruber, & Zaslavsky, 2011;Sawatzky, Ratner, Kopec, & Zumbo, 2012;Wall, …”